Once you subscribe to the podcast, the app itself polls the podcast’s feed and the audio is played directly from the host’s website.
You can also add a podcast directly if you know the feed url.
On top of all that, there has been a freely available API to the podcast directory for years that other podcast players use.
If you want to see a wall garden for podcasts, see Spotify, Google, etc.
[1] https://venturebeat.com/2019/07/16/apple-will-reportedly-fun...
https://www.giantbomb.com/podcast-xml/premiumbombcast?api_ke... (you just copy it from the RSS button on their site)
(previously it was https://username:[email protected]/podcast-xml/prem...)
Seems to work across most apps. I don't see why it would be that hard to build a standard around something similar.
[1] primarily ad-free versions of their main podcasts, but they also have premium-exclusive podcasts